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\begin{frame}
  \frametitle{Disproving Semantic Entailment}
  
  \begin{block}{}
    How to disprove $ \alpha_1,\ldots,\alpha_n \;\models \; \beta$?
    \pause
    That is, $ \alpha_1,\ldots,\alpha_n \;\nmodels \; \beta$?
    \bigskip
    \pause
    
    Find a valuation (assignment of truth values to variables)
    that 
    \begin{itemize}
      \item makes $\alpha_1,\ldots,\alpha_n$ true, and
      \item $\beta$ false.
    \end{itemize}
  \end{block}
  \pause
  
  \begin{exampleblock}{}
    Do we have \quad $p \vee q \;\models\; p \to q$ \quad ?
    \pause
    
    \begin{center}
    \begin{tabular}{|c|c|c|c|}
      \hline
      \thd $p$ & \thd $q$ & \thd $p \vee q$ & \thd $p \to q$ \\
      \hline
      $\F$ & $\F$ & $\F$ & $\T$\\
      \hline
      $\F$ & $\T$ & $\T$ & $\T$\\
      \hline
      $\T$ & $\F$ & \malert{1}{3}{$\T$} & \malert{1}{3}{$\F$}\\
      \hline
      $\T$ & $\T$ & $\T$ & $\T$\\
      \hline
    \end{tabular}
    \end{center}
    \pause\pause
    When $p$ is $\T$ and $q$ is $\F$, 
    then $p \vee q$ is $\T$ and $p \to q$ is $\F$. 
    \pause\medskip
    
    Conclusion: $p \vee q \;\not\models\; p \to q$\;.
  \end{exampleblock}
\end{frame}